The Obama administration’s top health official, making her first Hill appearance in almost a month, was eager to show the health care law had turned a corner after two rocky months. But she struggled to answer GOP lawmakers’ questions about policy cancellations that so far outpace enrollments — less than two weeks before the Dec. 23 deadline to sign up for coverage starting Jan. 1.

HHS on Wednesday released improved, but still lackluster, Obamacare signup numbers for November. About 260,000 people enrolled in federal and state Obamacare exchanges in November, bringing the two-month total to 365,000 people — still well below the administration’s goals for the first two months. More than 803,000 people also qualified for Medicaid during that time.

Sebelius cited recent positive trends in enrollment, helped by a better functioning website — and she announced that she had ordered an internal review at HHS into how the launch was so badly botched and how the agency can better manage big IT projects and contractors in the future.

The newest HHS signup numbers didn’t include how many people have actually paid their first month’s premiums, the last crucial step before completing enrollment.

“Our concern is that 364,000 number is fraudulent because it’s not those who have purchased plans yet,” said Rep. John Shimkus (R-Ill.) during the Energy and Commerce Health Subcommittee hearing.

The administration won’t know until early next year how many people completed enrollment, Sebelius said, because Dec. 31 is the deadline to pay for coverage starting January. “Some may have paid, some may have not,” she said, noting that payments are made directly to insurers and not HHS.

Sebelius pushed back when pressed by Republican lawmakers who said 5.6 million people had received cancellation notices in the past few months. “I don’t know where that number comes from,” she said when Rep. Joe Pitts (R-Pa.) cited news reports of millions of people losing coverage.

“Insurers cancel plans each and every year,” she added. “They change plans, they change networks.”

Sebelius cited some improving trends in enrollment and public interest. HHS said an additional 2 million people through November have been cleared to buy an exchange plan but haven’t picked one yet. There were 39.1 million visits to HealthCare.gov and state-run exchange websites in the first two months.

The website’s application process has been running more smoothly since the administration said it fixed the site for the vast majority of users at the end of November, but a surge of demand is expected as the Dec. 23 deadline approaches. And many users still find enrollment slow and frustrating.

Republican lawmakers pressed Sebelius about the accuracy of application files that insurers are receiving from HealthCare.gov and state-run health insurance exchanges. After weeks of media scrutiny, the administration last week said about 10 percent of the application files, known as the “834” files, sent to insurers currently contain erroneous information – down from about 25 percent in October.

“Who is going to guarantee that the doctor that sees the patient on Jan. 4 is actually covered for that visit?” asked Rep. Michael Burgess (R-Texas) incredulously.

There are errors, Sebelius acknowledged, but she said the administration is working closely with insurers to ensure that people who think they have coverage starting Jan. 1 will be insured.

“We are in the process of hand-matching individuals with insurance companies,” Sebelius said.

The back-end systems allowing HHS to pay out coverage subsidies to insurers won’t be ready until mid-January, Sebelius said. Insurers “are very comfortable” with the plan they worked out with HHS, she said.

The HHS secretary, the face of the bungled HealthCare.gov rollout, faced an avalanche of questions about ongoing and potentially future problems even though the hearing was sparsely attended. Congress is wrestling with a new budget plan unveiled Tuesday night and some lawmakers had traveled to South Africa for Nelson Mandela’s funeral.

Before the hearing, Sebelius announced a probe into how the president’s signature legislation stumbled out of the gate.

“Now that the website is working more smoothly, I’ve determined it’s the right time to better understand the structural and managerial policies that lead to the flawed launch,” Sebelius told the committee.

HHS Inspector General Dan Levinson has been asked to review the performance of contractors who built the faulty Obamacare enrollment website, as well as the department’s businesses practices that contributed to the disastrous launch.

The Centers for Medicare and Medicaid Services, the agency overseeing HealthCare.gov, will also create a chief risk officer position, and CMS will also take steps to improve contractor training and oversight after a seemingly poor lack of communication among federal officials and the dozens of companies who built parts of the website.

The administration has so far spent $319 million on HealthCare.gov, Sebelius disclosed Wednesday. HHS has $677 million budgeted for the website through October 2014, she said.

CMS deputy administrator Gary Cohen, who oversees exchanges, told a separate House committee Wednesday that the administration doesn’t yet have enrollment numbers for small business exchanges, known as SHOP. The administration two weeks ago announced a one-year delay in SHOP enrollment through HealthCare.gov, but small businesses can still sign up with an agent or broker or directly through an insurer.

“Because we haven’t been taking enrollments online, we don’t have those figures in the small business market,” Cohen told the House Small Business Committee. “The data will be reported to us by the insurance companies on a regular basis as they’re signing people up.”